Question: $P(x)=2x^4-x^3+2x^2-6$ What is the remainder when $P(x)$ is divided by $(x-2)$ ?
Solution: We can use the polynomial remainder theorem to solve this problem: For a polynomial $p(x)$ and a number $a$, the remainder on division by $x-a$ is $p(a)$. According to the theorem, the remainder when $P(x)$ is divided by $(x-{2})$ is $P({2})$ : $\begin{aligned} P({2})&=2({2})^4-({2})^3+2({2})^2-6 \\\\ &=2\cdot 16-8+2\cdot 4-6 \\\\ &=26 \end{aligned}$ In conclusion, the remainder when $P(x)$ is divided by $(x-2)$ is $26$.